Let X Poisson(), and suppose the maximum likelihood estimate of based on X is b

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Let X ∼ Poisson(λ), and suppose the maximum likelihood estimate of λ based on X is λb = 30 with 95% confidence interval (19, 41). Say whether each of the following statements is true or false. If it is false, say what is wrong with it.

a. About 95% of the time, the true value of λ lies between 19 and 41.

b. For about 95% of samples, the true value of λ lies in the confidence interval.

c. The confidence interval changes for every sample, but λ

stays the same.

d. The probability that a 95% confidence interval encloses λ

is about 0.95 under repeated sampling.

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Mathematics And Statistics For Science

ISBN: 9783031053177

1st Edition

Authors: James Sneyd, Rachel M. Fewster, Duncan McGillivray

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Question Posted: Sep 21, 2024 02:03 PM

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Let X Poisson(), and suppose the maximum likelihood estimate of based on X is b

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Mathematics And Statistics For Science

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